(B) First,simplify the fraction inside the bracket by multiplying the numerator and denominator by the conjugate of the denominator $(1-i)$:$\frac{2i}

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(B) First,simplify the fraction inside the bracket by multiplying the numerator and denominator by the conjugate of the denominator $(1-i)$:$\frac{2i}{1+i} = \frac{2i(1-i)}{(1+i)(1-i)} = \frac{2i - 2i^2}{1 - i^2} = \frac{2i + 2}{1 + 1} = \frac{2(i+1)}{2} = i+1$.Now,square the result:$(i+1)^2 = i^2 + 1^2 + 2i = -1 + 1 + 2i = 2i$.Therefore,the correct option is $B$.